I wonder if Mr Bennet would have visited a new neighbour even if there were no Bennet daughters? It seems a polite thing to do -- would it be rude not to pay a call? Could Bingley have visited the Bennets without having either an invitation or an earlier visit from Mr Bennet?

But I do like your idea, and I shall have to think about it. I do think that Mr Bennet might have been able to size up Bingley fairly quickly and determine that Lizzy was not very compatible with him.